For over half a century various digital communication techniques have been developed to address reliable transmission over imperfect links. These developments include information theory, practical source and channel coding schemes, and various effective modulation techniques. Many different channel models are considered in the literature extensively, and devised solutions have been put to efficient practical use; impacting all aspects of the world we live in today. Random insertions and/or deletions in addition to other, better understood, channel impairments (e.g. noise, intersymbol interference, etc.) are of utmost concern in many modern digital communication systems, including recording channels, transmissions through the Internet, character recognition systems, covert communications, and so on. The presence of insertions/deletions is often the bottleneck for more efficient reliable communications and higher areal densities in recording. Despite many advances over the past fifty years, channels with deletions/insertions are still far from being fully understood. To give a simple example, the capacity of a binary deletion channel is still unknown, and no practical coding/decoding schemes with performance close to available theoretical bounds are available.
This project studies insertion/deletion channels from both an information theoretic point of view, and a channel coding perspective. Specifically, it involves development of novel information theoretic results and practical coding schemes for such channels, with extensions to channels with intersymbol interference, additive noise, and other impairments. Capacity approaching low density parity check (LDPC) and turbo coding schemes are considered. In addition, a new set of interesting problems involving insertions/deletions over wireless fading channels, including multi-input multi-output (MIMO) communications, are formulated, and solutions are developed.
